Pith Number

pith:ZCHHB7V3

pith:2010:ZCHHB7V3IV52D6OKRBGQL532IO

not attested not anchored not stored refs pending

Random walk on surfaces with hyperbolic cusps

Colin Guillarmou, Hans Christianson, Laurent Michel

arxiv:1005.2754 v1 · 2010-05-16 · math.SP · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZCHHB7V3IV52D6OKRBGQL532IO}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T02:07:18.527406Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c88e70febb457ba1f9ca884d05f77a43bac7f078a3ed5460bedf87512e19d52f

Aliases

arxiv: 1005.2754 · arxiv_version: 1005.2754v1 · doi: 10.48550/arxiv.1005.2754 · pith_short_12: ZCHHB7V3IV52 · pith_short_16: ZCHHB7V3IV52D6OK · pith_short_8: ZCHHB7V3

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZCHHB7V3IV52D6OKRBGQL532IO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c88e70febb457ba1f9ca884d05f77a43bac7f078a3ed5460bedf87512e19d52f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9366e60c98e50b0a6a70b5657fcf9d59c4c1a36cea083817d4e2319ef8c562e3",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-05-16T14:53:44Z",
    "title_canon_sha256": "9c01a50b14638ae0a8c6d43cacaede048fcada6e5967851e9b512bb8abfd4d2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.2754",
    "kind": "arxiv",
    "version": 1
  }
}